How do I differentiate (e^(2x)+1)^3?

You might be tempted to start by expanding the brackets, but in this case it's much easier to use the chain rule. This is the rule that, to differentiate f(g(x)), we find f'(g(x))*g'(x). In other words, to differentiate a function of a function of x, we first differentiate the 'outside' function while leaving the 'inside' function unchanged; then we differentiate the 'inside' function; then we multiply the two together. In this case, the inside function (g) is the e^(2x)+1 and the outside function (f) is the 'cubed'. Therefore, f'(g(x)) = 3(e^(2x)+1)^2, and g'(x) = 2(e^(2x)). So:(d/dx)((e^(2x)+1)^3) = (3(e^(2x)+1)^2) * 2(e^(2x)) = 6((e^(2x)+1)^2)(e^(2x))

AH
Answered by Alfie H. Maths tutor

3753 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the first 3 terms, in ascending powers of x, of the binomial expansion of (2 – 9x)^4 giving each term in its simplest form.


Where does the circle equation come from?


Solve the ODE y' = -x/y.


Find the stationary points on y = x^3 + 3x^2 + 4 and identify whether these are maximum or minimum points.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences